physics (specification a) pa10 unit 10 the synoptic unit · general certificate of education june...
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General Certificate of EducationJune 2005Advanced Level Examination
PHYSICS (SPECIFICATION A) PA10Unit 10 The Synoptic Unit
Monday 27 June 2005 Afternoon Session
In addition to this paper you will require:! a calculator;! a pencil and a ruler.
Time allowed: 2 hours
Instructions! Use blue or black ink or ball-point pen. ! Fill in the boxes at the top of this page. ! Answer all questions in the spaces provided. All working must be shown.! Do all rough work in this book. Cross through any work you do not want
marked.
Information! The maximum mark for this paper is 80. ! Mark allocations are shown in brackets. ! The paper carries 20% of the total marks for Physics Advanced.! A Data Sheet is provided on pages 3 and 4. You may wish to detach this
perforated sheet at the start of the examination. ! You are expected to use a calculator where appropriate.! In questions requiring description and explanation you will be assessed on
your ability to use an appropriate form and style of writing, to organise relevant information clearly and coherently, and to use specialist vocabularywhere appropriate. The degree of legibility of your handwriting and the levelof accuracy of your spelling, punctuation and grammar will also be taken intoaccount.
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Data Sheet
! A perforated Data Sheet is provided as pages 3 and 4 of this question paper.
! This sheet may be useful for answering some of the questions in the examination.
! You may wish to detach this sheet before you begin work.
Answer all questions.
1 A winch in a boatyard uses a 230 V electric motor to raise objects from a boat onto the quayside, asshown in Figure 1.
Figure 1
(a) The winch takes 22 s to raise an object of mass 160 kg through a height of 5.0 m. The motorcurrent during this time is 14 A. Calculate the efficiency of the winch.
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(b) (i) The steel cable that is used to raise the 160 kg object has a cross-sectional area of 1.8 × 10�4m2. Calculate the strain in the cable when it raises the object at constantspeed.
the Young modulus for steel = 2.1 × 1011Pa
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(ii) The length of steel cable from the object to the winch is 14 m when the object is on theboat. Calculate the extension of the cable when it supports the object.
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2 (a) Suggest two reasons why an α particle causes more ionisation than a β particle of the same initialkinetic energy.
You may be awarded marks for the quality of written communication in your answer.
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(b) A radioactive source has an activity of 3.2 × 109Bq and emits α particles, each with kineticenergy of 5.2 MeV. The source is enclosed in a small aluminium container of mass 2.0 × 10�4kgwhich absorbs the radiation completely.
(i) Calculate the energy, in J, absorbed from the source each second by the aluminiumcontainer.
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(ii) Estimate the temperature rise of the aluminium container in 1 minute, assuming no energyis lost from the aluminium.
specific heat capacity of aluminium = 900 J kg�1K�1
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3 A wind turbine, as shown in Figure 2, has blades of length 22 m. When the wind speed is 15 m s�1 itsoutput power is 1.5 MW.
Figure 2
(i) The volume of air passing through the blades each second can be calculated byconsidering a cylinder of radius equal to the length of the blade. Show that 2.3 × 104m3
of air passes through the blades each second.
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(ii) Calculate the mass of air that passes through the blades each second.
density of air = 1.2 kg m�3
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(iii) Calculate the kinetic energy of the air reaching the blades each second.
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(iv) Assuming that the power output of the turbine is proportional to the kinetic energy ofthe air reaching the blades each second, discuss the effect on the power output if thewind speed decreased by half.
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4 A steel wire of diameter 0.24 mm is stretched between two fixed points 0.71 m apart. A U-shaped magnetis placed at the centre of the wire so that the wire passes between its poles, as shown in Figure 3.
Figure 3
(a) (i) Explain why the wire vibrates when an alternating current is passed through it.
You may be awarded marks for the quality of written communication in your answer.
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(ii) Explain why the wire vibrates strongly in its fundamental mode when the frequency of thealternating current is 290 Hz.
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(iii) Show that the speed of the waves on the wire is 410 m s�1.
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stretchedwire
ac supply
magnet
ac supply
stretchedsteelwire
(b) The speed, c, of waves on a wire of mass per unit length, µ, is related to the tension, T, in thewire by
(i) The wire in Figure 3 is at a tension of 60 N. Calculate its mass per unit length.
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(ii) Hence calculate the density of the metal.
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.µTc =
5 Whilst investigating the oscillations of a helical spring, a student carried out measurements whenvarious masses were suspended from the spring. For each mass, the length l of the spring wasmeasured and 50 vertical oscillations were timed. The results are shown in the table.
(a) Complete the table. (2 marks)
(b) The time period for vertical oscillations is given by
where m is the mass suspended and k is the spring constant.
(i) Assuming that the spring obeys Hooke�s law, show that
T 2 = 4π2 (l � l0) g
where l0 is the length of the unloaded spring.
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(ii) Plot a graph of T 2 against l.
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length l/mm time for 50 time period T 2/s2
oscillations/s T/s
316 12.5 0.25 0.063
333 17.5
349 22.0
364 25.5
381 28.5
397 31.0
,2kmT π=
,
(iii) Use the graph to determine values for g and l0.
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(c) Estimate the value of l which would give a time period of 1.00 s. State and explain one reasonwhy the behaviour of the spring may cause your estimated value to be incorrect.
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6 Figure 4 shows a sonar device suspended by a cable from a helicopter. The device is used to detectsubmarines.
Figure 4
(a) With the device below the water surface, it emits pulses of sound at a constant rate. After eachpulse is transmitted, it is used to detect pulses reflected by underwater objects. Figure 5 shows a screen display of the reflected pulses received for each transmitted pulse.
Figure 5
(i) Pulse P is due to partial reflection from the surface directly above the sonar. A furtherpulse R is observed. Pulse R is due to a reflection by a submarine. Calculate thedistance from the submarine to the sonar.
speed of sound in seawater = 1500 m s�1
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0 2 4 6 8 10
Ptransmitted pulse
time/s
sonarwater surface
R
P
time/s
(ii) Discuss how the display shown in Figure 5 would differ if the distance to the submarinehad been half the value calculated in part (a) (i).
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(b) Figure 6 shows the sonar device raised out of the water to a fixed height above the surface.
Figure 6
(i) Calculate the critical angle for sound waves in air at the surface.
speed of sound in air = 340 m s�1
speed of sound in the seawater = 1500 m s�1
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(ii) Explain why sound waves from the sonar device cannot enter the water beyond a certaindistance from the device. Assume the water surface is flat.
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sonar
water surface
7 (a) (i) At the surface of a spherical planet of radius R, show that the gravitational potential, Vs , isrelated to the gravitational field of strength, gs, by
Vs = �gs R.
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(ii) The gravitational field strength of the Moon at its surface is 1.6 N kg�1. Show that thegravitational potential energy of an oxygen molecule at the surface is �1.4 × 10�19J.
radius of the Moon = 1700 kmmolar mass of oxygen = 0.032 kg mol�1
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(b) Oxygen gas at 400 K is released on the surface of the Moon.
(i) Calculate the mean kinetic energy of an oxygen gas molecule at this temperature.
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(ii) The maximum temperature of the surface of the Moon is about 400 K. Use the dataopposite and the results of your calculations to explain why some of the oxygen gasreleased at the Moon�s surface would escape into space.
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8 The hydrogen atom may be represented as a central proton with an electron moving in a circular orbitaround it as shown in Figure 7. When the atom is in the ground state, the radius of the electron�s orbitis 5.3 × 10�11m.
Figure 7
(a) By applying this model to the hydrogen atom in the ground state, calculate
(i) the force of electrostatic attraction between the electron and the proton,
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(ii) the speed of the electron,
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(iii) the ratio of the de Broglie wavelength of the electron to the circumference of the orbit.
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orbit
electron
proton +
�
(b) The total energy of the electron in a hydrogen atom may be shown to have discrete values given, in J, by
E = � ,
where n = 1 for the ground state, n = 2 for the first excited state, and so on.
(i) Calculate the wavelength of the light emitted when the electron returns to the ground statefrom the first excited state.
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(ii) Explain why visible light will not be produced by any transition in which the electronreturns to the ground state.
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END OF QUESTIONS
2.2 × 10�18
n2
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